Simplify 3/(3-3/(x+3))-3/(3+3/(x+3))

$\frac{3}{3 - \frac{3}{x + 3}} - \frac{3}{3 + \frac{3}{x + 3}}$

Simplify each term.

Cancel the common factor of $3$ and $3 - \frac{3}{x + 3}$ .

Rewrite $3$ as $- 1 (- 3)$ .

$\frac{3}{- 1 (- 3) - \frac{3}{x + 3}} - \frac{3}{3 + \frac{3}{x + 3}}$

Factor $- 1$ out of $- \frac{3}{x + 3}$ .

$\frac{3}{- 1 (- 3) - (\frac{3}{x + 3})} - \frac{3}{3 + \frac{3}{x + 3}}$

Factor $- 1$ out of $- 1 (- 3) - (\frac{3}{x + 3})$ .

$\frac{3}{- 1 (- 3 + \frac{3}{x + 3})} - \frac{3}{3 + \frac{3}{x + 3}}$

Factor $3$ out of $3$ .

$\frac{3 \cdot 1}{- 1 (- 3 + \frac{3}{x + 3})} - \frac{3}{3 + \frac{3}{x + 3}}$

Cancel the common factors.

Factor $3$ out of $- 1 (- 3 + \frac{3}{x + 3})$ .

$\frac{3 \cdot 1}{3 (- 1 (- 1 + \frac{1}{x + 3}))} - \frac{3}{3 + \frac{3}{x + 3}}$

Cancel the common factor.

$\frac{3 \cdot 1}{3 (- 1 (- 1 + \frac{1}{x + 3}))} - \frac{3}{3 + \frac{3}{x + 3}}$

Rewrite the expression.

$\frac{1}{- 1 (- 1 + \frac{1}{x + 3})} - \frac{3}{3 + \frac{3}{x + 3}}$

Cancel the common factor of $1$ and $- 1$ .

Rewrite $1$ as $- 1 (- 1)$ .

$\frac{- 1 (- 1)}{- 1 (- 1 + \frac{1}{x + 3})} - \frac{3}{3 + \frac{3}{x + 3}}$

Move the negative in front of the fraction.

$- \frac{1}{- 1 + \frac{1}{x + 3}} - \frac{3}{3 + \frac{3}{x + 3}}$

Simplify the denominator.

To write $- 1$ as a fraction with a common denominator, multiply by $\frac{x + 3}{x + 3}$ .

$- \frac{1}{- 1 \cdot \frac{x + 3}{x + 3} + \frac{1}{x + 3}} - \frac{3}{3 + \frac{3}{x + 3}}$

Combine $- 1$ and $\frac{x + 3}{x + 3}$ .

$- \frac{1}{\frac{- (x + 3)}{x + 3} + \frac{1}{x + 3}} - \frac{3}{3 + \frac{3}{x + 3}}$

Combine the numerators over the common denominator.

$- \frac{1}{\frac{- (x + 3) + 1}{x + 3}} - \frac{3}{3 + \frac{3}{x + 3}}$

Reorder terms.

$- \frac{1}{\frac{1 - (x + 3)}{x + 3}} - \frac{3}{3 + \frac{3}{x + 3}}$

Rewrite $\frac{1 - (x + 3)}{x + 3}$ in a factored form.

Apply the distributive property.

$- \frac{1}{\frac{1 - x - 1 \cdot 3}{x + 3}} - \frac{3}{3 + \frac{3}{x + 3}}$

Multiply $- 1$ by $3$ .

$- \frac{1}{\frac{1 - x - 3}{x + 3}} - \frac{3}{3 + \frac{3}{x + 3}}$

Subtract $3$ from $1$ .

$- \frac{1}{\frac{- x - 2}{x + 3}} - \frac{3}{3 + \frac{3}{x + 3}}$

Multiply the numerator by the reciprocal of the denominator.

$- (1 \frac{x + 3}{- x - 2}) - \frac{3}{3 + \frac{3}{x + 3}}$

Multiply $\frac{x + 3}{- x - 2}$ by $1$ .

$- \frac{x + 3}{- x - 2} - \frac{3}{3 + \frac{3}{x + 3}}$

Cancel the common factor of $3$ and $3 + \frac{3}{x + 3}$ .

Factor $3$ out of $3$ .

$- \frac{x + 3}{- x - 2} - \frac{3 \cdot 1}{3 + \frac{3}{x + 3}}$

Cancel the common factors.

Factor $3$ out of $3$ .

$- \frac{x + 3}{- x - 2} - \frac{3 \cdot 1}{3 (1) + \frac{3}{x + 3}}$

Factor $3$ out of $\frac{3}{x + 3}$ .

$- \frac{x + 3}{- x - 2} - \frac{3 \cdot 1}{3 \cdot 1 + 3 \frac{1}{x + 3}}$

Factor $3$ out of $3 \cdot 1 + 3 \frac{1}{x + 3}$ .

$- \frac{x + 3}{- x - 2} - \frac{3 \cdot 1}{3 \cdot (1 + \frac{1}{x + 3})}$

Cancel the common factor.

$- \frac{x + 3}{- x - 2} - \frac{3 \cdot 1}{3 \cdot (1 + \frac{1}{x + 3})}$

Rewrite the expression.

$- \frac{x + 3}{- x - 2} - \frac{1}{1 + \frac{1}{x + 3}}$

Simplify the denominator.

Write $1$ as a fraction with a common denominator.

$- \frac{x + 3}{- x - 2} - \frac{1}{\frac{x + 3}{x + 3} + \frac{1}{x + 3}}$

Combine the numerators over the common denominator.

$- \frac{x + 3}{- x - 2} - \frac{1}{\frac{x + 3 + 1}{x + 3}}$

Add $3$ and $1$ .

$- \frac{x + 3}{- x - 2} - \frac{1}{\frac{x + 4}{x + 3}}$

Multiply the numerator by the reciprocal of the denominator.

$- \frac{x + 3}{- x - 2} - (1 \frac{x + 3}{x + 4})$

Multiply $\frac{x + 3}{x + 4}$ by $1$ .

$- \frac{x + 3}{- x - 2} - \frac{x + 3}{x + 4}$

To write $- \frac{x + 3}{- x - 2}$ as a fraction with a common denominator, multiply by $\frac{x + 4}{x + 4}$ .

$- \frac{x + 3}{- x - 2} \cdot \frac{x + 4}{x + 4} - \frac{x + 3}{x + 4}$

To write $- \frac{x + 3}{x + 4}$ as a fraction with a common denominator, multiply by $\frac{- x - 2}{- x - 2}$ .

$- \frac{x + 3}{- x - 2} \cdot \frac{x + 4}{x + 4} - \frac{x + 3}{x + 4} \cdot \frac{- x - 2}{- x - 2}$

Write each expression with a common denominator of $(- x - 2) (x + 4)$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{x + 3}{- x - 2}$ by $\frac{x + 4}{x + 4}$ .

$- \frac{(x + 3) (x + 4)}{(- x - 2) (x + 4)} - \frac{x + 3}{x + 4} \cdot \frac{- x - 2}{- x - 2}$

Multiply $\frac{x + 3}{x + 4}$ by $\frac{- x - 2}{- x - 2}$ .

$- \frac{(x + 3) (x + 4)}{(- x - 2) (x + 4)} - \frac{(x + 3) (- x - 2)}{(x + 4) (- x - 2)}$

Reorder the factors of $(x + 4) (- x - 2)$ .

$- \frac{(x + 3) (x + 4)}{(- x - 2) (x + 4)} - \frac{(x + 3) (- x - 2)}{(- x - 2) (x + 4)}$

Combine the numerators over the common denominator.

$\frac{- (x + 3) (x + 4) - (x + 3) (- x - 2)}{(- x - 2) (x + 4)}$

Simplify the numerator.

Factor $- (x + 3)$ out of $- (x + 3) (x + 4) - (x + 3) (- x - 2)$ .

$\frac{- (x + 3) (x + 4 - x - 2)}{(- x - 2) (x + 4)}$

Subtract $x$ from $x$ .

$\frac{- (x + 3) (0 + 4 - 2)}{(- x - 2) (x + 4)}$

Add $0$ and $4$ .

$\frac{- (x + 3) (4 - 2)}{(- x - 2) (x + 4)}$

Subtract $2$ from $4$ .

$\frac{- (x + 3) \cdot 2}{(- x - 2) (x + 4)}$

Multiply $2$ by $- 1$ .

$\frac{- 2 (x + 3)}{(- x - 2) (x + 4)}$

Simplify with factoring out.

Move the negative in front of the fraction.

$- \frac{(2) (x + 3)}{(- x - 2) (x + 4)}$

Factor $- 1$ out of $- x$ .

$- \frac{2 (x + 3)}{(- (x) - 2) (x + 4)}$

Rewrite $- 2$ as $- 1 (2)$ .

$- \frac{2 (x + 3)}{(- (x) - 1 (2)) (x + 4)}$

Factor $- 1$ out of $- (x) - 1 (2)$ .

$- \frac{2 (x + 3)}{- (x + 2) (x + 4)}$

Simplify the expression.

Rewrite $- (x + 2)$ as $- 1 (x + 2)$ .

$- \frac{2 (x + 3)}{- 1 (x + 2) (x + 4)}$

Move the negative in front of the fraction.

$- - \frac{2 (x + 3)}{(x + 2) (x + 4)}$

Multiply $- 1$ by $- 1$ .

$1 \frac{2 (x + 3)}{(x + 2) (x + 4)}$

Multiply $\frac{2 (x + 3)}{(x + 2) (x + 4)}$ by $1$ .

$\frac{2 (x + 3)}{(x + 2) (x + 4)}$

Simplify 3/(3-3/(x+3))-3/(3+3/(x+3))

Related Questions

Support LCMGCF.com by disabling your adblocker.